COMP 232 Lecture Notes - Lecture 2: Commutative Property, Contraposition, Idempotence

• School: Concordia University
• Department: Computer Sci.
• Course: COMP 232
• Professor: Gosta Grahne

Document Summary

A tautology is a compound proposition that is. True for all truth values of the atomic propo- sitions in it. A contradiction is a compound proposition that is false for all truth values of the atomic propositions in it. A contingency is a proposition which is nei- ther a tautology nor a contradiction. Two compound propositions p, q are logically equivalent if p q is a tautology. Two compound propositions p, q are logically equivalent if they have the same truth table. Is the proposition p q logically equivalent to the proposition p q? a. P q p q q p. Since the last column is all true, we have p q p q. Are the compound propositions (p q) (q p) and p q logically equivalent? a q p q q p a b p q b p. Since the two righ-most columns are the same: (p q) (q p) p q.